How make hair using textures
The biggest thing missing in your screenshot is transparency.
To achieve this you probably want connect up the hair texture alpha channel to the alpha channel of your diffuse texture (I am assuming this is where it is stored, otherwise you may need an extra texture from somehere). Additionally, if you are using Eevee, you will also need the set the blend mode to Alpha Hashed in the material settings.
You may find this answer useful:
How can I make an image plane have transparency in Eevee with nodes?
And as @ChristopherBennett mentioned in the comments, you shpuld set your normal map strength to 1.